Topological Computer Graphics

	http://swiss.csail.mit.edu/~jaffer/Geometry/Marbling
	Topological Computer Graphics

Sophisticated computer-generated images tend to be rendered from exhaustively detailed geometries of no import -- except that simpler forms are not pleasing to the eye.

Ink Marbling

The marbling effect sometimes used to pattern fabrics or book endpapers manifests the transits of the ink-plowing combs as intricate folds of continuous filaments of color. Different viscosities of ink would alter the contour curvatures, but not the character of the marbling. How can one produce marbling mathematically without introducing lots of computational artifice?

Presented here are practical methods for visualizing topologically stretchy deformations of the plane.

Mathematical Ink Marbling

Serpentine Marbling

Scallops and Clams

Marbling the Torus

Textile Designs

Transfer Effects

Dropping Ink

Gallery

Fractals?
The Mandelbrot set and related curves display banding, but have only a couple parameters affecting them. These couple parameters change disparate features throughout the image. Although one can affect the drawing, one cannot control it.
Also, fractals' self-similarity down to infinitesimal scales is more akin to the Horned Sphere counterexample than to the simply connected homeomorphisms explored here.

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		Geometry
	agj @ alum.mit.edu	Go Figure!